"Je SUIS de France, d'Angleterre" expresses where you are from.
"Je VIENS de la France, de l'Angleterre" expresses the action; the fact that you actually travelled from France or England to wherever the destination.
Note that there are some exceptions; there are some countries/islands that are said in French with "des", "de la", or "du".
If someone asks the question "Tu es d'où?" meaning "Where are you from?", depending on where the person lives, it could be different:
Je suis/viens DE LA Guadeloupe, DES États-Unis, DU Congo.
I come from Guadeloupe, the United States, Congo.
So in this case, it expresses where you are from because of the question asked before.
However, still with the exceptions, if the question had been "Tu viens d'où?", it would have been trickier to fully understand which one to use since both "suis" and "viens" are used in "casual" speech to answer this question.
In casual speech, "Tu viens d'où?" can talk about where you are from or the action of travelling.
Note that it should normally be "Tu es d'où?" when asking "Where are you from?", and "Tu viens d'où?" When asking for information about a destination/place.
With those exceptions, the context is important to know whether the person is talking about where s/he is from or the action of travelling.
Hope that makes sense!